A Bit More About “Extra Dimensions”

A while ago I was writing a sequence of articles — interrupted for some weeks by all the hullabaloo over Higgs particles and all the noise about neutrinos — concerning the possibility that the world has more than the three spatial dimensions that are obvious to us.  These “extra” dimensions seem to be very confusing to non-experts, so I’ve been trying to find a way to make them seem a little less strange.  We’ll see if I’ve succeeded.  Building on my articles describing some types of worlds of 1 spatial dimension and of 2 spatial dimensions, I’ve now written an article giving one type of example of an “extra” dimension.   Other articles to follow over coming weeks will provide other examples of extra dimensions, as well as an attempt to explain how scientists can potentially look for evidence of an extra dimension.

14 responses to “A Bit More About “Extra Dimensions”

  1. This dimension issue is the rock bottom foundation for physics. When how many dimensions this universe has is known, the physics will be complete.

    Of course, what is dimension? And, what are its attributes? What those attributes got to do with the universe?

    First, we should look what are already known.
    1. In 1870s, Georg Cantor proved that every n-dimensional space can always be brought into a one-to-one correspondence with the one dimensional line, that is, one dimensional line can give rise to n-dimensional space.

    2. This dimensionality issue can also be understood with fractal geometry. In fractal geometry, there are many space-filling curves, an infinite number of them to be exact. With the Hilbert space-filling curve, it crosses every point on a plane without crossing itself, that is, a two dimensional plane is reduced to a one dimensional line.

    From two facts above, all high-dimensions can always be reduced to one-dimension.

    Your explanation about dimension is truly inspirational, especially for the spatial dimension in terms of physics. However, we should look the definition of dimension in a bigger scope, in general term.

    New definition: If “all” information of system B can be “wholly” described with n codes, then system B has n dimensions.

    The above definition is a linguistics definition. Yet, it is similar to the base-dimension of a vector space, and it is in line with your saying, Matt: “A location inside a two-dimensional space is specified by two pieces of information.”

    With this new definition, the entire world must change.
    1. Regardless of how many physical dimensions it has, the entire computable world has only two-dimensions, as it can be wholly described with two codes (such as, [0, 1]). This is guaranteed with the Two-code theorem of mathematics.

    2. The outer surface of a ball has 4 dimensions, guaranteed with the four-color theorem.

    3. The outer surface of a torus has 7 dimensions, calculated by the edge-equations or the Heawood Conjecture.

    Then, how many dimensions does the non-computable world have? If we know how many dimensions the infinity has, then the physics will be complete.

    With this new definition, the consciousness and the intelligence could be dimensions, even the dimensions for the non-computable world. Of course, this statement will make a wonderful day for the crackpot callers, and they will reach their ecstasy on this.

    However, your example of boat/canal has hinted that consciousness could be a necessary gateway for the manifestation of an extra dimension although the consciousness itself might not be a dimension.

  2. Since my last comment here, I received an email with a simple question, “How can this new definition of dimension be any use in physics?” If Matt allows, the following is a short answer.

    Physics must encompass “all” realities and must go way beyond some forces and a particle zoo. The linguistics definition on dimension is able to address the dimensionality of all systems, including the abstract systems. That is, the concept of dimension is a thread weaving through all systems and is a means of unifying all systems into a unified framework.

    For example, the attribute of “individuality” of every person is taken for granted by all of us. The concept of individuality of life was way beyond the scope of physics before. Now, the four-color theorem guarantees that countable number of balls can be produced with individuality, that is, no two balls have the same surface pattern. Thus, if life has four dimensions, then it is a topological ball, and its individuality will be guaranteed by the four-color theorem. Are we surprised that every individual life, indeed, has four dimensions (the four genetic codes, [A, G, T, C]) with this new definition? With 4 dimensions, the individuality of every individual life is guaranteed.

    Obviously, 4 codes are not enough for a species. For a bisexual species, it needs 7 codes (among the three additional codes, two to identify the two sexes and one to identify the new generation). Of course, for a cloning species, 5 codes are enough. As lives roam in the 4 spacetime dimensions, those 7 life dimension is not a part of these spacetime dimensions. In short, this universe (with life) should have 11 (= 7 + 4) dimensions.

    The anthropic principle (AP) was only a principle of philosophy before. Now, by knowing the exact dimensions of lives, this AP becomes a principle of physics. If a particle zoo theory describes a zoo having less than 7 dimensions, it cannot be the foundation for the rising of life, and thus must be wrong. If a theory describes a zoo having more than 7 dimensions, then what the heck are those additional dimensions for?

    I hope that I have clarified my last comment a bit.

    • Hi Tienzen,

      it`s the first time I read about such “life dimensions” here from You, so this concept seems a bit strange or “esoteric” to me …
      Is it right that the total of 11 dimensions with 7 extra “life dimensions” has nothing to do with M-theory and the corresponding 7 extra “space dimensions” and the agreement of the numbers is just a coincidence?

  3. Ok, you throw away terms like “consciousness” and “intelligence” without carefully defining them. What the heck are “consciousness” and intelligence ? What do you understand them to be ? And how could them be “dimensions” of anything ?

    • Read carefully: neither consciousness nor intelligence are defined, in the text, to be “dimensions”. Indeed they are NOT dimensions. The directions across, along, and down into the canal are the dimensions.

      Consciousness and intelligence are important, however, in discussing extra dimensions, because extra dimensions are intuitively confusing to most people. Through our experience, we all grow up believing the world has three spatial dimensions, the ones we can see in, move around in, and conceive of in our minds. If in fact the world has four or even more dimensions, it is important to understand WHY we believe something about nature that is actually wrong.

      If we were not conscious and intelligent, we would have no picture of the world and there would be nothing to discuss. All science is done by conscious intelligent creatures, and much of science is about learning how and why our brains’ view of the world is mistaken.

  4. And Id like to throw my 2c on this:

    Quoting Tienzen (Jeh-Tween) Gong
    “However, your example of boat/canal has hinted that consciousness could be a necessary gateway for the manifestation of an extra dimension”

    My interpretation of Matt’s example with the quasi 1D is totally different then yours. No “consciousness” is needed for the extra dimension to manifest itself. It is intrinsically manifest in the region where it’s physics is relevant. It doesnt need superior mammals to manifest itself, no more than gravity needed us to keep Earth in orbit around the sun. If it’s there, it’s there, regardless if the universe is populated by amoebas or by animals with a sufficiently developed frontal cortex to build a particle accelerator, which may one day allow then to infer it;s existence.

    • Ok,ok — let’s keep on the narrow path here. Consciousness is ONLY necessary here in illustrating that in developing a picture of the world it is possible to make a mistake, in which one’s brain is led to think that the world has fewer dimensions than in actually has.

      But consciousness has NOTHING to do with the geometry of the world itself!!!

      I’m just trying to explain why you might think the world has three dimensions whereas in fact it might have four or five or ten or twenty-six.

      I’m now sorry I introduced consciousness so cavalierly into the article. Clearly I did it poorly and I’m going to have to rewrite it.

      • Matt, in my opinion your article is very well written and it doesn’t need a rewrite. It is perfectly readable and it is not ambiguous. I see that I made a mistake not quoting Tienzen (Jeh-Tween) Gong in my first reply. My query to define consciousness and intelligence and how can be “dimensions” where addressed to him not to you.

  5. To Tienzen (Jeh-Tween) Gong:
    If you strongly believe in your ideas, perhaps you should start your own blog. Otherwise, please, take pity on those of us who come to this site to hear what Matt has to say.

  6. Sergei Petrov, sorry for offending you with my comments. I did know that my second comment is a bit over the line as a comment. Thanks for Matt’s tolerance.